In the big courtyard, enter the southeast portion to lower a lift down. Step off of it, then get back on and return to the starting point to find a soul sphere, a backpack, a megaarmor, and the yellow key. All four lowered columns that had these things count as one secret. (sector 14)

After you get the yellow key, use the yellow door at the bottom of the lift to reach the next room. Use the misaligned wall to the north, then open the next two doors behind it to find a medikit and a switch. The switch reveals a cacodemon, another medikit, and a super shotgun. (sector 23)

This is the sector with the blue key. To reach it, first shoot the barrels in the big room with the two blue doors, which will get rid of the barrels beyond the cage as well. Then head into the room with the teleporter (mentioned in Secret #6 below) and take it. You will be in the caged room, hopefully not stuck between barrels. Use the skull switch and leave the room via the teleporter, then backtrack to the big room to get the blue key. (sector 105)

In the nukage room with three switches, flip the middle switch to lower the three, then get onto the right switch and go off of its north end to trigger a lift to the southeast (an arrow of armor bonuses points in that direction as a hint). This will net you a megasphere, a berserk pack, and boxes of shotgun shells. (sector 125)

Use the doors south of the red keycard to reach a room with a teleporter. Ignore the teleporter and use the wall that has a skull on it. Use the next set of doors to reach a room with cacodemons and a soul sphere in it. There are two secrets to find here. (sector 145)

See Secret #6. (sector 147)

In the nukage room with three switches, flip the left switch to lower the passage to the south with spectres. The wall with the skull on it hides a rocket launcher and a lost soul. (sector 148)

When you reach the exit area at the west end of the courtyard, climb the steps to the top, which will cause a lift to lower. Quickly reenter the courtyard and go to where the stage area with the switch is, where a teleporter will be. Enter this teleporter before it rises to reach a secret area with several supplies and monsters. If you have the red key, go to the far end to get a BFG9000. (sector 179)